Question

Consider the equation 6x+15=−3(ax−b), where a and b are real numbers. Which values for a and b will result in the equation having an infinite number of solutions?

Answer 1

a=-2 and b=5.

To have an infinite number of solutions, the two sides must be identical.

6x+15=-3(ax-b)

Using the distributive property,
6x+15=-3*ax--3*b
6x+15=-3ax+3b

This means -3ax=6x and 3b=15;
-3ax=6x

Divide both sides by -3:
-3ax/-3 = 6x/-3
ax=-2x

Divide both sides by x:
ax/x=-2x/x
a=-2

3b=15

Divide both sides by 3:
3b/3=15/3
b=5